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Ruddelsden-Popper halide perovskites are highly versatile quasi-two-dimensional energy materials with a wide range of tunable optoelectronic properties. Here we use the all-inorganic Cs$_{n+1}$Pb$_n$X$_{3n+1}$ Ruddelsden-Popper perovskites with X=I, Br, and Cl to systematically model the effect of octahedral tilting distortions on the energy landscape, band gaps, macroscopic polarization, and the emergence of Rashba-/Dresselhaus splitting in these materials. We construct all unique $n=1$ and $n=2$ structures following from octahedral tilts and use first-principles density functional theory to calculate total energies, polarizations and band structures, backed up by band gap calculations using the $GW$ approach. Our results provide design rules for tailoring structural distortions and band-structure properties in all-inorganic Ruddelsden-Popper perovskites through the interplay of the amplitude, direction, and chemical character of the antiferrodistortive distortion modes contributing to each octahedral tilt pattern. Our work emphasizes that, in contrast to 3D perovskites, polar structures may arise from a combination of octahedral tilts, and Rashba-/Dresselhaus splitting in this class of materials is determined by the direction and Pb-I orbital contribution of the polar distortion mode.